Declarative approach to NURBS surface design: from semantic to geometric models

Present days modelling systems most often consider B-Spline and NURBS surfaces for B-rep (boundary representation) modelling of objects. The designer has to manipulate a lot of control points which is often complex and tedious. Declarative approach of surface modelling aims at providing high level tools for design. The designer gives to the system a description, set of geometric, topological or physical properties and the declarative modeller produces several geometric solutions corresponding to the given constraints and features. This paper introduces the different models involved in the declarative approach of NURBS surface and their relationships. An example illustrates the use of the different data structures.